Here I will illustrate how to use the complex exponential to derive some useful trigonometric identities. Lets start with the Euler identities:

(1)

(2)

Now put in equation (1) and use the rule for multiplication of exponentials:

(3)

Dedicated to those who never had the opportunity to receive a good education

Dedicated to those who never had the opportunity to receive a good education

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# Mathematical appendices

Here I will illustrate how to use the complex exponential to derive some useful trigonometric identities. Lets start with the Euler identities:

(1)

(2)

Now put in equation (1) and use the rule for multiplication of exponentials:

(3)

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